Grossinho M., Tersian S. An Introduction to Minimax Theorems and Their Applications to Differential Equations

Springer, 2001. — 273 Pages. — ISBN: 144194849XThe book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind:
To present a survey of existing minimax theorems,
To give applications to elliptic differential equations in bounded domains,
To consider the dual variational method for problems with continuous and discontinuous nonlinearities,
To present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities,
To study homoclinic solutions of differential equations via the variational methods.
The contents of the book consist of seven chapters, each one divided into several sections.
Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization.Minimization and Mountain-Pass Theorems.
Saddle-Point and Linking Theorems.
Applications to Elliptic Problems in Bounded Domains.
Periodic Solutions for Some Second-Order Differential Equations.
Dual Variational Method and Applications.
Minimax Theorems for Locally Lipschitz Functionals and Applications.
Homoclinic Solutions of Differential Equations.
Notations.